1. Field of Invention
The present invention relates to a method of characterizing the similarity between measurements on entities. The invention also relates to a computer program product and a data carrier comprising such computer program product.
2. Related Art
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g., comprising part of, one, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
Manufacturing a typical device by a lithographic process typically includes a plurality of cycles of various types of steps. These steps may include coating the substrate with a photosensitive material (or otherwise applying a photosensitive material to one or more surfaces of the substrate), projecting an image on the photosensitive material, developing the photosensitive material and processing the substrate, which can include covering the substrate in a new layer of material. One of the problems that may be encountered with the lithographic process is that successive layers are not accurately imaged on top of each other so that there is a so-called overlay error. In order to avoid proceeding onto the subsequent steps when an overlay error already exists which would be detrimental to the component's performance, after each cycle the overlay error may be measured. If the overlay error is too large then the most recent layer can be removed and that step repeated before proceeding onto the next step.
In order to reduce overlay error, substrates are generally provided with a plurality of reference marks so that the position of the substrate on a substrate table in a projection apparatus may be measured very precisely prior to the exposure operation. In this way it is possible to improve the accuracy of the exposure operation because the relative positions of the substrate, the previously applied patterned layer and the patterning device in the lithographic apparatus may be determined.
Another problem with multi-cycle lithographic processes is the deformation of the substrate which can occur with the application of particular layers and/or particular patterns. Deformation includes, for example, topographic 3-dimensional deformation, deformation of the reference marks (shape or depth) or variation of layer properties or thicknesses deposited on the substrate. Chemical mechanical polishing (CMP) is notorious for causing deformation of the substrate. With the use of substrates with a diameter of 300 mm or more, it is expected that substrate deformation may become an even more important factor. In order to reduce deformation, it may be desirable to keep the processes as uniform as possible over the whole area of the substrate. Deformation of the substrate may lead to errors in the imaging of the substrate resulting in the need to repeat a particular operation. Also, during the development of a process for a particular component manufactured by lithography, the process may be optimized to minimize, or at least keep within limits, the amount of substrate deformation. The reduction of overlay error or an error as a result of substrate deformation, or at least early detection of one or more of such errors, may lead to improved yield.
Small particles present on the surface of the substrate may hamper the lithographic process since at the positions of the particles no proper illumination of the substrate can be achieved. Generally the size of the particles is such that they cannot be detected by the level sensors present in the lithographic apparatus, but they may be detected when more accurate level sensors are employed, for instance in dedicated measurement equipment of the manufacturer of the substrate.
Small particles may also be present between the substrate carrier, i.e. the support table or chuck, and the substrate. These particles may deform the layers before the lithographic process is performed.
The particles cause artifacts, so-called focus spots, in the subsequent layers arranged at the surface of the substrate. When the artifacts are positioned beneath an alignment mark, they may give rise to overlay errors as well. A timely detection of the artifacts, i.e. a detection before the next layer is applied on the substrate, may lead to an improved yield.
One option would be to measure the substrate at least parts of the grids and/or substrate shapes of a number of substrates in separate (off-line) measuring instruments (metrology tools) or on-line in the lithographic apparatus itself, just before a pattern is to be applied on the substrate, and show the results of the measurements in graphical representations. Such a graphical representation typically comprises a huge amount of data. Therefore, the graphical representations practically can not be analyzed and interpreted by a human operator. The interpretation based on graphical representations of the measured substrate grid and shape is rather subjective and time-consuming and does not provide a workable situation for defining substrate-shape, substrate-grid and substrate field-shape consistency given the huge amount of measurement data. This hampers process characterization, criteria for transfer to production, and production quality monitoring.